Fig. 2: FEM validation of MTF.

a Schematics of a string resonator illuminated by a light source (red) at the center. At steady-state, a temperature difference ΔT from the frame temperature T₀, will arise upon photothermal heating. b String’s thermal conductance G as a function of the point-like heat source relative position x/L, for three different lengths (0.1, 1, and 10 mm). Circles: FEM results of G in the mean temperature framework (MTF). Solid curve: MTF theoretical calculation (15). c Comparison between FEM results (circles) and model (solid curve) for the relative power responsivity (3) as a function of the string length. d Comparison between FEM results (circles) and model (solid curve) for the thermal time constant (4) as a function of the string length. e Schematics of a drumhead resonator. For the comparison with the FEM, an equivalent circular geometry is used to reduce the problem complexity. f Circular drumhead’s MTF thermal conductance for 0.1, 1, and 10 mm side length. g Relative power responsivity comparison for drumheads. h Thermal time constant comparison for drumheads. Solid curve: theory (4). Blue crosses: response time of the FEM peak temperature ΔT_FEM for uniform heating (UH). Black crosses: response time of ΔT_FEM for local heating (LH). Purple squares: response time of the surface mean temperature \(\left\langle \Delta {T}_{FEM}\right\rangle\) for LH. Black circles: response time of the resonance frequency \({f}_{{0}_{FEM}}\) for LH. i Schematics of a trampoline resonator. j Trampolines' MTF thermal conductance for a frame window side length of 1.1 mm and five different central pad side lengths. The model (solid curve) accounts here for a heat source impinging only in the central pad. k Relative power responsivity comparison for trampolines. l Thermal time constant comparison for trampolines. Model and FEM used parameters for all the designs: ρ = 3000 kg/m³, c_p = 700 J/(kg K), κ = 2.7 W/(mK), E = 250 GPa, σ₀ = 200 MPa, ν = 0.23, α_th = 1.23 ppm/K, ϵ_rad = 0.05, α = 0.5%, w = 5 μm, h = 50 nm^30,61. For all the FEM simulations, a Gaussian beam of waist w₀ = 1 μm has been used